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Abstract and Applied Analysis
Volume 2016, Article ID 9238948, 9 pages
http://dx.doi.org/10.1155/2016/9238948
Research Article

Global Existence of Weak Solutions to a Fractional Model in Magnetoelastic Interactions

1Laboratoire MISI, FST Settat, Université Hassan I, 26000 Settat, Morocco
2Laboratoire M2I, FST Errachidia, Equipe MAMCS, Université Moulay Ismaïl, BP 509, Boutalamine, 52000 Errachidia, Morocco

Received 6 July 2016; Accepted 8 September 2016

Academic Editor: Cemil Tunç

Copyright © 2016 Idriss Ellahiani et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The paper deals with global existence of weak solutions to a one-dimensional mathematical model describing magnetoelastic interactions. The model is described by a fractional Landau-Lifshitz-Gilbert equation for the magnetization field coupled to an evolution equation for the displacement. We prove global existence by using Faedo-Galerkin/penalty method. Some commutator estimates are used to prove the convergence of nonlinear terms.